Slant Curve in Lorentzian BCV Spaces

Journal of Geometry and Symmetry in Physics ◽

10.7546/jgsp-56-2020-67-85 ◽

2020 ◽

Vol 56 ◽

pp. 67-85

Author(s):

Abdullah Yildirim ◽

Keyword(s):

Directional Derivative ◽

Lorentzian Manifolds ◽

Slant Curve ◽

Slant Curves

The aim of this study is to examine the slant curves in Lorentzian manifolds with BCV (Bianchi-Cartan-Vranceanu) metrics. A practical form of the directional derivative in the presence of the BCV metrics is presented. Moreover, some theorems for slant curves in Lorentzian BCV manifolds are proved.

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Slant Curves and Contact Magnetic Curves in Sasakian Lorentzian 3-Manifolds

Symmetry ◽

10.3390/sym11060784 ◽

2019 ◽

Vol 11 (6) ◽

pp. 784 ◽

Cited By ~ 1

Author(s):

Ji-Eun Lee

Keyword(s):

Three Dimensional ◽

Lorentzian Manifold ◽

Cross Product ◽

Slant Curve ◽

Magnetic Curve ◽

Three Space ◽

Slant Curves

In this article, we define Lorentzian cross product in a three-dimensional almost contact Lorentzian manifold. Using a Lorentzian cross product, we prove that the ratio of κ and τ − 1 is constant along a Frenet slant curve in a Sasakian Lorentzian three-manifold. Moreover, we prove that γ is a slant curve if and only if M is Sasakian for a contact magnetic curve γ in contact Lorentzian three-manifold M. As an example, we find contact magnetic curves in Lorentzian Heisenberg three-space.

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C-parallel and C-proper slant curves of S-manifolds

Filomat ◽

10.2298/fil1919305g ◽

2019 ◽

Vol 33 (19) ◽

pp. 6305-6313

Author(s):

Şaban Güvenç ◽

Cihan Özgür

Keyword(s):

Normal Bundle ◽

Legendre Curve ◽

Slant Curve ◽

Slant Helix ◽

Slant Curves

In the present paper, we define and study C-parallel and C-proper slant curves of S-manifolds. We prove that a slant curve in an S-manifold of order r ? 3, under certain conditions, is C-parallel or C-parallel in the normal bundle if and only if it is a non-Legendre slant helix or Legendre helix, respectively. Moreover, under certain conditions, we show that is C-proper or C-proper in the normal bundle if and only if it is a non-Legendre slant curve or Legendre curve, respectively. We also give two examples of such curves in R2m+s(-3s).

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SLANT CURVES AND PARTICLES IN THREE-DIMENSIONAL WARPED PRODUCTS AND THEIR LANCRET INVARIANTS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972712000809 ◽

2012 ◽

Vol 88 (1) ◽

pp. 128-142 ◽

Cited By ~ 5

Author(s):

CONSTANTIN CĂLIN ◽

MIRCEA CRASMAREANU

Keyword(s):

Vector Field ◽

Three Dimensional ◽

Curvature Vector ◽

Warping Function ◽

Warped Products ◽

Slant Curve ◽

Lancret Invariant ◽

Legendre Curves ◽

Frenet Curvatures ◽

Slant Curves

AbstractSlant curves are introduced in three-dimensional warped products with Euclidean factors. These curves are characterised by the scalar product between the normal at the curve and the vertical vector field, and an important feature is that the case of constant Frenet curvatures implies a proper mean curvature vector field. A Lancret invariant is obtained and the Legendre curves are analysed as a particular case. An example of a slant curve is given for the exponential warping function; our example illustrates a proper (that is, not reducible to the two-dimensional) case of the Lancret theorem of three-dimensional hyperbolic geometry. We point out an eventuality relationship with the geometry of relativistic models.

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A framework for pulmonary fissure segmentation in 3D CT images using a directional derivative of plate filter

Signal Processing ◽

10.1016/j.sigpro.2020.107602 ◽

2020 ◽

Vol 173 ◽

pp. 107602 ◽

Cited By ~ 1

Author(s):

Hong Zhao ◽

Berend C. Stoel ◽

Marius Staring ◽

M. Bakker ◽

Jan Stolk ◽

...

Keyword(s):

Directional Derivative ◽

Ct Images ◽

3D Ct ◽

Fissure Segmentation ◽

Plate Filter

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Four-dimensional homogeneous Lorentzian manifolds

Monatshefte für Mathematik ◽

10.1007/s00605-013-0588-9 ◽

2013 ◽

Vol 174 (3) ◽

pp. 377-402 ◽

Cited By ~ 7

Author(s):

Giovanni Calvaruso ◽

Amirhesam Zaeim

Keyword(s):

Lorentzian Manifolds

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FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887806001739 ◽

2006 ◽

Vol 03 (07) ◽

pp. 1349-1357 ◽

Cited By ~ 17

Author(s):

V. V. KOZLOV ◽

I. V. VOLOVICH

Keyword(s):

Mass Spectrum ◽

Elliptic Equations ◽

Gordon Equation ◽

Infinite Family ◽

De Sitter ◽

Lorentzian Manifolds ◽

Klein Gordon ◽

Finite Action ◽

Discrete Mass ◽

Klein Gordon Equation

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

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A Partial Derivative Approach to the Change of Scale Formula for the Function Space Integral

Entropy ◽

10.3390/e23010026 ◽

2020 ◽

Vol 23 (1) ◽

pp. 26

Author(s):

Young Sik Kim

Keyword(s):

Fourier Transform ◽

Function Space ◽

Partial Derivative ◽

Directional Derivative ◽

Feynman Integral ◽

Wiener Integral ◽

Vector Calculus ◽

Change Of Scale

We investigate the partial derivative approach to the change of scale formula for the functon space integral and we investigate the vector calculus approach to the directional derivative on the function space and prove relationships among the Wiener integral and the Feynman integral about the directional derivative of a Fourier transform.

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